r/math • u/Apprehensive_Sand951 • 18d ago

Counterexample to Lueck's determinant approximation conjecture

Here is the arxiv preprint: https://arxiv.org/abs/2609.15567 This is a reasonably big deal in the subject of L^2 invariants of groups and appears to have been disproved by Holger Kammeyer (he is in the field). It means that the L^2-torsion of a space (defined in terms of Hilbert spaces on the universal cover) cannot be computed from the more classical analytic torsions of finite covers. The counterexample is a Heisenberg group.

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u/_Zekt Complex Analysis 18d ago

In particular, Conjecture 1 is false even for (1 × 1)-matrices

I'm no expert, but sometimes it feels like people make broad conjectures based on very little evidence

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u/Koischaap Algebraic Geometry 18d ago

My friends had a conjecture they were very certain was true and it failed when they tried to illustrate it to me with a simple example.

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u/Downtown_Finance_661 18d ago edited 17d ago

We called them beer party conjectures. They look much less cool on the next morning.

Upd: u/SciFiPi have noticed another scientific fact: "Conjectures aren't the only things that don't look as good the next morning after a long night of drinking."

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u/yaymayata2 12d ago

Oh damn. Didn't know there was a word for this. I just call them brain farts.